Designing acceptance sampling schemes for life testing with mixed censoring

Mixed censoring is useful extension of Type I and Type II censoring and combines some advantages of both types of censoring. This paper proposes a general Bayesian framework for designing a variable acceptance sampling scheme with mixed censoring. A general loss function which includes the sampling cost, the time‐consuming cost, the salvage value, and the decision loss is employed to determine the Bayes risk and the corresponding optimal sampling plan. An explicit expression of the Bayes risk is derived. The new model can easily be adapted to create life testing models for different distributions. Specifically, two commonly used distributions including the exponential distribution and the Weibull distribution are considered with a special decision loss function. We demonstrate that the proposed model is superior to models with Type I or Type II censoring. Numerical examples are reported to illustrate the effectiveness of the method proposed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

成败型产品的Bayes鉴定试验方案研究

利用可靠性增长模型给出了成败型产品鉴定试验的一种Bayes方法.提出了Bayes鉴定试验的最大后验风险准则,利用这种准则制定的鉴定试验方案综合了产品研制过程中的先验信息.在确保产品质量的前提下,与传统的鉴定试验方案相比,将大大节省试验时间.     

Designing an optimal life test with type I censoring

The present study considers the design of an optimal life test plan with Type I censoring in the case where only one testing machine is available and a machine tests items sequentially as seen in fatigue life tests of metallic materials. Under the condition that the life test is conducted in a fixed censoring time and with a fixed number of test items, a method for determining the censoring time and the number of test items is proposed from the Bayesian point of view. The proposed method is also applied to the Weibull life distribution with a known shape parameter.     

小子样条件下基于Normal-Poisson过程的性能可靠性评定

对于高可靠、长寿命产品,基于性能退化数据分析可靠性是一种行之有效的技术途径。结合航空航天产品性能退化的机理与现场试验小子样的特点,建立了基于Normal-Poisson过程的性能退化模型。论文在对产品性能退化建模的基础上,结合Bayes方法给出了退化模型参数的估计算法和可靠性推断的公式,最后结合实例说明了方法的有效性。     

Stepwise inspection in Bayesian multiattribute acceptance sampling

Bayesian models for multiattribute acceptance sampling have been developed under the assumption that sampling inspection is carried to completion. A Bayesian multiattribute model for stepwise sampling inspection is proposed, whereby sampling inspection is terminated as soon as the disposition of the inspection lot is determined. An iterative solution procedure is developed for obtaining optimal or near-optimal multiattribute acceptance sampling plans under stepwise sampling inspection. The effect of stepwise sampling inspection on the characteristics of an optimal sampling plan is investigated. It is shown that stepwise sampling inspection achieves a sampling plan with lower total expected cost than complete sampling inspection. In addition, it is shown that the sequence of attributes in a stepwise sampling inspection substantially affects the sampling plan and resultant expected cost. The proposed methodology is used to evaluate various heuristics which may be used to determine the sequence of attributes in a stepwise inspection procedure.     

基于最大后验风险的多层Bayes方法

为了对指数型产品进行可靠性鉴定,首先给出了失效率的多层先验分布,然后从最大后验风险的角度,运用Bayes方法,制定出可靠性鉴定试验方案.按照此鉴定试验方案,缩短了试验时间,从而降低了鉴定试验所需的费用.     

评定舰炮武器系统可靠性指标MTBF的Bayes方法

为解决目前舰炮武器系统可靠性试验时间长、样本量小、双方风险高的实际问题,提出了基于验前信息评定舰炮武器系统可靠性MTBF的Bayes方法,充分挖掘了验前信息资源,有效缩短了试验时间,经仿真计算表明,在同等现场试验条件下,采用该方法可大幅降低可靠性试验双方风险。     

指数型产品可靠性验收试验的一种贝叶斯方法

采用贝叶斯方法 ,利用大量的历史数据和工程技术人员的丰富经验确定先验分布 ,制定出验收试验的一种新方案 .按照这一方案 ,在确保产品质量的前提下 ,可大大节省试验时间 ,从而得到十分可观的经济效益 .     

武器系统MTBF的Bayes序贯检验方法

针对武器系统试验鉴定中显著具有的小子样的特点,研究了武器系统平均故障间隔时间(MTBF)的Bayes序贯检验方法,推导了检验模型,平均试验数计算公式、定时和定数截尾实际风险计算公式,并给出了算例。该方法在武器系统可靠性鉴定中具有一定的应用价值。     

Risk preference,multiple attributes,and multiple criteria in bayesian acceptance sampling plans

Although there has been considerable research directed toward developing Bayesian acceptance sampling plans, little consideration has been given to incorporating a decision-maker's risk attitude or treating such problems in terms of multiple-type defects and multiple criteria. We review our own work which is focused on the above issues. A model incorporating risk preference is shown to yield substantial differences in the characteristics of an optimal sampling plan relative to a typical Bayesian linear cost (risk neutral) model. Bayesian models and optimization schemes for a variety of multiple-type defect plans are reviewed. A bicriterion acceptance model, employing average outgoing quality and average inspection cost is also formulated. Traditional versus interactive optimization procedures are compared empirically in terms of ease of use, satisfaction with solutions, and insight gained into the problem.     

Information theory for ranking and selection

We study the classical ranking and selection problem, where the ultimate goal is to find the unknown best alternative in terms of the probability of correct selection or expected opportunity cost. However, this paper adopts an alternative sampling approach to achieve this goal, where sampling decisions are made with the objective of maximizing information about the unknown best alternative, or equivalently, minimizing its Shannon entropy. This adaptive learning is formulated via a Bayesian stochastic dynamic programming problem, by which several properties of the learning problem are presented, including the monotonicity of the optimal value function in an information-seeking setting. Since the state space of the stochastic dynamic program is unbounded in the Gaussian setting, a one-step look-ahead approach is used to develop a policy. The proposed policy seeks to maximize the one-step information gain about the unknown best alternative, and therefore, it is called information gradient (IG). It is also proved that the IG policy is consistent, that is, as the sampling budget grows to infinity, the IG policy finds the true best alternative almost surely. Later, a computationally efficient estimate of the proposed policy, called approximated information gradient (AIG), is introduced and in the numerical experiments its performance is tested against recent benchmarks alongside several sensitivity analyses. Results show that AIG performs competitively against other algorithms from the literature.     

基于贝叶斯模型的装备剩余寿命预测研究

为了解决武器装备日益复杂及维修工作日趋繁重的问题,运用贝叶斯模型预测装备修理后的剩余寿命,为合理安排其修理计划提供依据。替代传统的指数分布,用威布尔分布描述系统寿命特征,并运用极大似然方法和贝叶斯方法估计威布尔分布的两个未知参数,给出其置信区间。在此基础上,对先验样本和后验样本两种不同情况,分别运用贝叶斯模型预测装备修理后的剩余寿命,并给出实例。结果表明了该方法的有效性。     

指数寿命产品可靠性增长试验的Bayes分析

针对指数寿命产品的定时、定数截尾试验方案,推广了Mazzuchi-Soyer模型的应用范围。首先引入模型假设,以狄氏分布作为先验分布,综合利用产品研制的历史信息和专家信息,结合产品研制各阶段试验数据,给出了各阶段可靠性的联合后验分布。然后利用Gibbs抽样算法解决后验推断计算问题,得到各阶段产品可靠性的Bayes点估计和区间估计。最后给出产品可靠性增长分析实例,表明了模型的优越性。     

Planning accelerated life tests for censored two‐parameter exponential distributions

We consider optimal test plans involving life distributions with failure‐free life, i.e., where there is an unknown threshold parameter below which no failure will occur. These distributions do not satisfy the regularity conditions and thus the usual approach of using the Fisher information matrix to obtain an optimal accelerated life testing (ALT) plan cannot be applied. In this paper, we assume that lifetime follows a two‐parameter exponential distribution and the stress‐life relationship is given by the inverse power law model. Near‐optimal test plans for constant‐stress ALT under both failure‐censoring and time‐censoring are obtained. We first obtain unbiased estimates for the parameters and give the approximate variance of these estimates for both failure‐censored and time‐censored data. Using these results, the variance for the approximate unbiased estimate of a percentile at a design stress is computed and then minimized to produce the near‐optimal plan. Finally, a numerical example is presented together with simulation results to study the accuracy of the approximate variance given by the proposed plan and show that it outperforms the equal‐allocation plan. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 169–186, 1999     

Optimum simple step-stress accelerated life tests for weibull distribution and type I censoring

This article presents an optimum simple step-stress accelerated life test for the Weibull distribution under Type I censoring. It is assumed that a log-linear relationship exists between the Weibull scale parameter and the (possibly transformed) stress and that a certain cumulative exposure model for the effect of changing stress holds. The optimum plan—low stress and stress change time—is obtained, which minimizes the asymptotic variance of the maximum likelihood estimator of a stated percentile at design stress. For selected values of the design parameters, nomographs useful for finding the optimum plan are given, and the effects of errors in preestimates of the parameters are investigated. As an alternative to the simple step-stress test, a three-level compromise plan is proposed, and its performance is studied and compared with that of the optimum simple step-stress test. © 1993 John Wiley & Sons. Inc.     

面向诸元计算精度鉴定的二次抽样试验设计方法

针对诸元计算精度常规试验方法的缺点和不足之处,提出了"二次抽样"的试验设计方法,在一次抽样的基础上,通过对试验结果进行分析,进行第二次有针对性的抽样试验,并采用贝叶斯估计方法,对两次相关联的试验结果进行综合评价。最后采用该方法对某型炮兵指控系统的诸元计算精度进行了检验,证明了该方法的实用性和有效性。与常规试验方法相比,二次抽样法对诸元计算中各变量不同值域的权重进行了重新分配,其计算结果对被试装备的实际性能更具有指向性。     

雷达情报特征的Bayes识别方法

根据雷达情报目标判性应用背景,对Bayes方法在该领域的应用进行了研究,初步建立了基于雷达情报特征的统计模型,并在算法的收敛速度和稳健性等方面与D-S证据理论进行了比较。仿真结果表明,Bayes方法对先验信息的精确程度要求并不十分严格,能较好地解决雷达情报综合问题。     

An empirical bayes estimator for the scale parameter of the two-parameter weibull distribution

An empirical Bayes estimator is given for the scale parameter in the two-parameter Weibull distribution. The scale parameter is assumed to vary randomly throughout a sequence of experiments according to a common, but unknown, prior distribution. The shape parameter is assumed to be known, however, it may be different in each experiment. The estimator is obtained by means of a continuous approximation to the unknown prior density function. Results from Monte Carlo simulation are reported which show that the estimator has smaller mean-squared errors than the usual maximum-likelihood estimator.     

Bayes sequential design of stock levels

Bayesian determination of optimal stock levels is studied for the case of Poisson distribution of the demand variable, and prior gamma distribution of the expected demand. Bayes sequential procedure is derived, assuming that stock level can be adjusted at the beginning of each period so that a shortage can be immediately replenished and an overstock can be corrected. The Bayes sequential procedure is more difficult to obtain if this assumption is removed. A dynamic programming method for obtaining the general Bayes sequential procedure is outlined. Finally, an empiric Bayes estimation procedure of the optimal Bayesian stock level is presented.     

基于贝叶斯网络分类器的雷达辐射源识别方法

雷达辐射源识别是电子对抗中的重要组成部分.贝叶斯网络分类器建立在坚实的理论基础之上,具有较为优秀的分类性能,而且能够有效地处理不确定性问题,重点研究了如何利用贝叶斯网络分类器进行雷达辐射源识别,并通过仿真实验对朴素贝叶斯分类器及其扩展方法进行了分析比较.实验结果表明,与基于概率近似准则的方法相比,基于分类准确率提高准则的扩展树生成方法具有更为优秀的分类性能.